Yes... by distancing yourself you are trying to protect your feelings but you never know what life is gonna throw at you. Hell, you might have the unfortunate luck of seeing her and her new FWB just by running an errand which equates to your day being totally ruined! But subjecting yourself to that situation willingly, makes things easier on you because you were already mentally prepared for it. It helps ya get a thick skin and that heart off of your sleeve. Win-win for you!

It depends on what you have to GAIN from the situation. I get uncomfortable in crowds, hell I can barely go to the grocery store. Unfortunately going outside my house is kind of a big deal, so I force myself to do it each and every time. I force myself to find ways to cope and since then my anxiety has improved greatly.

What do you have to gain from being around this girl? Sure you can tell yourself all day that she's cool and neat or whatever but let's face it - there's a lot of girls that are like that without the baggage. To be honest, I think that you want her to "come to her senses" and see how awesome you are. So you're going to continue to be "friends" with her, make yourself suffer through whatever it takes in the hopes that it'll work out between the two of you. But really? That's not going to happen.

You have nothing to gain. Move on bro. You did the right thing the first time - telling her you don't want to be a part of her life.

I kind of agree with Kitsune. My thought about exposing yourself to things that you are uncomfortable with is sweets. I love candy and ice cream etc. I don't keep it in the house because it won't last very long and I will feel pathetic for not having more will power. I can walk past these things in the grocery store without being devastated because I know I will see them there and that it's not good for me to expose myself to them. I think this girl is your ice cream. Stay away and let time works it magic. If you see her out, you see her out and it may sting a bit. You can feel empowered by knowing that she is with him because you made a conscious effort to seperate her from your life.

All I read is: "blah blah blah I still want to hang around her because I can't let her go."
To me it looks more like constantly reopening a scar before it has time to heal, and make it bleed constantly, if anything.

- "I think its better to put yourself in the uncomfortable situation": what situation are you talking about? Also, if I follow your reasoning correctly, you should be taking baths of acid every day.
I think the problem is that you normally wouldn't/shouldn't be exposed to this situation - should you chose to, so it's pointless to become "resistant to" this situation (being near a girl you like too much, or diving in acid), whereas you are susceptible to be subjected to your phobias in your daily life, without a choice in the matter (for example agoraphobia as it was mentioned earlier), so it's worth investing some effort in fighting them.
See, I'd rather learn how to play guitar than spend time with a girl I don't want to spend time with. That seems like a more productive use of my time really. You're lucky to have so much spare time!

- "I wanna get over that mindset of me "erasing" people from my life because they end up making me feel uncomfortable.": depends on your feelings for her, if you can be friend with someone - fine. I'm never uncomfortable with my friends though, so I doubt if I were in your situation I would consider her as a friend.
Anyway, remember that every minute you will be wasting with this girl is one minute you didn't spend finding the future love of your life, or improving for her.